how to use logartihmic differentiation to solve y=sqrt(x^(2)-1...

\[y=\sqrt{(x ^{2}}-1 / x ^{2}+1)\]

any11???

take the natural log of both sides first... and then, simplify the right side to 1/2 ln (x^2-1) /(x^2+1) now differentiate the right side. at the end, be sure to multiply the original equation to the right side because when you take the natural log of the original y, it's turned into a y'/y

when you take the natural log of both sides first, the equation should look like (y'/y)=1/2 ln (x^2-1) /(x^2+1)

didnt understand the last 2 steps..can u show them?

after differentiating the right side using the rule d/dx=ln u=u'/u, you'll get (y'/y) = 1.2 * u'/u you want the answer to what y' equals, so you have to multiply both sides by y (the original equation ) to cancel out the y under the y'

n thts it?..so final ans will hav a y in it?

it's this sqrt(x^2−1/x2+1)

so final ans is...?

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